Rewrite as a simplified fraction. ${3.\overline{31} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 331.3131...\\ 1x &= 3.3131...\end{align*}}$ Subtracting the two equations, we have: ${99x = 328}$ ${x = \dfrac{328}{99}} \text{or} {3 \dfrac{31}{99}}$